(e) Sketch the graph of h by hand. (d) Use function notation to write h in terms of the parent function f. h(x)=(x−2)^3+5

Describe the transformations that must be applied to $y=x^2$ to create the graph of each of the following functions.
a) ${\displaystyle y=\frac{1}{4}{(x-3)}^2+9}$
b) ${\displaystyle y={\left(\left(\frac{1}{2}\right)x\right)}^2-7}$

Graph f and g in the same rectangular coordinate system. Use transformations of the graph of f to obtain the graph of g. Graph and give equations of all asymptotes. Use the graphs to determine each functions

Graph f and g in the same rectangular coordinate system. Use transformations of the graph off to obtain the graph of g. Graph and give equations of all asymptotes. Use the graphs to determine each function’s domain and range.
${\displaystyle f\left(x\right)=\ln x\text{and}g⟨x)=-\ln \left(2x\right)}$

For ${\displaystyle y=-{\log }_{2}x}$.
a) Use transformations of the graphs of ${\displaystyle y={\log }_{2}x}$ and ${\displaystyle y={\log }_{3}x}$ o graph the given functions.
b) Write the domain and range in interval notation.
c) Write an equation of the asymptote.

An observational study is retrospective if it considers only existing data. It is prospective if the study design calls for data to be collected as time goes on. Tell which of the following observational studies are retrospective and which are prospective. To see whether crime mes are related to moon phase, a researcher looks at ten years of archived police blotter reports and compares them with moon charts from the same period.

Begin by graphing ${\displaystyle f\left(x\right)={\log }_{2}x}$ Then use transformations of this graph to graph the given function. What is the graphs